Israeli security forces are carrying out operations to rescue hostages taken by Palestinian militants from Gaza and clear areas they seized on Saturday.
The military said troops had secured 22 locations in southern Israel but were still sweeping through another eight.
The surprise attack by hundreds of gunmen from Hamas, under the cover of intense rocket fire, has reportedly killed at least 300 people in Israel.
More than 310 people in Gaza have been killed in retaliatory Israeli strikes.
On both sides, thousands of people have been injured, many seriously.
Israeli Prime Minister, Benjamin Netanyahu, told Israelis on Saturday night that they were going into a “long and difficult war”. He also warned Hamas, which governs Gaza, that its hideouts would be reduced to “rubble”.
Hamas leader Ismail Haniyeh said it was on the “verge of a great victory”.